Understanding Graphing Translations of Absolute Value Functions

This video tutorial explains how to graph translations of the basic absolute value function. It covers the standard form of the function, y = |x - h| + k, where a = 1. The video discusses the characteristics of the graph, such as its V shape and vertex at the origin. It explains how the values of h and k affect the graph's position, with h shifting it left or right and k shifting it up or down. The tutorial includes animations and examples to illustrate these concepts, and concludes with a preview of the next video, which will cover more complex functions with both h and k values.

What is the standard form of an absolute value function when a = 1?

• y = |x - h| + k

• y = |x + h| - k

• y = a|x - h| + k

• y = a|x + h| - k

What shape does the graph of a basic absolute value function take?

• U shape

• V shape

• L shape

• W shape

How does a positive h value affect the graph of an absolute value function?

• Shifts the graph down

• Shifts the graph up

• Shifts the graph left

• Shifts the graph right

What is the vertex of the graph of an absolute value function in terms of h and k?

• (0, 0)

• (h, k)

• (k, h)

• (1, 1)

If h is negative, in which direction is the graph shifted?

• Right

• Left

• Down

• Up

In the equation y = |x + 3|, what is the value of h?

• 1

• 0

• -3

• 3

How is the graph of y = |x - 1| different from the basic absolute value function?

• Shifted down 1 unit

• Shifted up 1 unit

• Shifted right 1 unit

• Shifted left 1 unit

What happens to the graph when k is positive?

• It shifts left

• It shifts right

• It shifts down

• It shifts up

If k is negative, how is the graph affected?

• It shifts left

• It shifts down

• It shifts up

• It shifts right

For the equation y = |x| - 4, what is the value of k?

• -4

• 4

• 0

• 1